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Mirrors > Home > ILE Home > Th. List > imaeq2 | Unicode version |
Description: Equality theorem for image. (Contributed by NM, 14-Aug-1994.) |
Ref | Expression |
---|---|
imaeq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reseq2 4886 | . . 3 | |
2 | 1 | rneqd 4840 | . 2 |
3 | df-ima 4624 | . 2 | |
4 | df-ima 4624 | . 2 | |
5 | 2, 3, 4 | 3eqtr4g 2228 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 crn 4612 cres 4613 cima 4614 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 df-opab 4051 df-xp 4617 df-cnv 4619 df-dm 4621 df-rn 4622 df-res 4623 df-ima 4624 |
This theorem is referenced by: imaeq2i 4951 imaeq2d 4953 ssimaex 5557 ssimaexg 5558 isoselem 5799 f1opw2 6055 fopwdom 6814 ssenen 6829 fiintim 6906 fidcenumlemrk 6931 fidcenumlemr 6932 sbthlem2 6935 isbth 6944 ennnfonelemp1 12361 ennnfonelemnn0 12377 ctinfomlemom 12382 ctinfom 12383 tgcn 13002 iscnp4 13012 cnpnei 13013 cnima 13014 cnconst2 13027 cnrest2 13030 cnptoprest 13033 txcnp 13065 txcnmpt 13067 metcnp3 13305 |
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